If $f: \mathbb{R} \rightarrow \mathbb{R}$ is such that $f(x+y) = f(x) + f(y)$ for all $x, y \in \mathbb{R}$,$f(1) = 7$,and $\sum_{r=1}^n f(r) = 14112$,then $n = $

Three rods of equal lengths are joined to form an equilateral triangle $ABC$. $D$ is the mid-point of $AB$. The coefficient of linear expansion is $\alpha_1$ for the material of rod $AB$ and $\alpha_2$ for the material of rods $AC$ and $BC$. If the distance $DC$ remains constant for small changes in temperature,then

If the change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below it,then (both $x$ and $h$ being much smaller than the radius of the earth)

The enthalpy of formation of ammonia is $-46.0 \, kJ \, mol^{-1}$. The enthalpy change for the reaction $2NH_{3(g)} \longrightarrow N_{2(g)} + 3H_{2(g)}$ is ..... $kJ \, mol^{-1}$.

The pressure versus temperature graph of an ideal gas is as shown in the figure. The density of the gas at point $A$ is ${\rho _0}$. The density at point $B$ will be

While a collector to emitter voltage is constant in a transistor,the collector current changes by $8.2 ~mA$ when the emitter current changes by $8.3 ~mA$. The value of forward current ratio is